Hospitals are where sick people go to get better. But sometimes, they're also where healthy people get sick.

Now, with a potentially severe flu season on the horizon, many hospitals are strengthening their vaccination policies and requiring workers who refuse the flu shot to wear surgical masks. Harrington HealthCare System this week became the latest organization to install a mask policy.

“Our first and foremost priority is to take care of our patients, and this is one way to do that,” said Edward H. Moore, Harrington's president and chief executive.

The health care system, which operates the 114-bed hospital in Southbridge, has told unvaccinated workers to wear masks when they're entering patient rooms or are within 3 feet of a patient.

UMass Memorial Medical Center in Worcester has a stricter policy: Workers who have not been vaccinated must wear masks throughout the hospital except for entryways, elevators, break rooms and the cafeteria.

Hospital administrators say the goal is purely to prevent the spread of a dangerous — sometimes deadly — virus.

The new policy at UMass Memorial appears to have swayed many workers to get the flu shot. Last flu season, the Worcester hospital had one of the worst vaccination rates in the state; less than 61 percent of its workers were vaccinated. This year, more than 90 percent of hospital staff received the flu shot.

But some say the masking policy goes too far, eroding workers' rights and doing nothing to prevent the spread of illness.

“I feel it's a bullying tactic,” said Ellen T. Smith, nurse and co-chairwoman of the nurses bargaining unit at the hospital's University Campus.

Ms. Smith has been wearing a mask, covering nose to chin, during her 12-hour shifts. “I do not receive the flu vaccine,” she said by phone from a nurses' convention in Las Vegas. “I just don't believe in it.”

David Schildmeier of the Massachusetts Nurses Association called masking policies “a scarlet letter approach” and said hospitals should worry about the infections that visitors — not nurses — might be carrying.

The flu vaccine is far from perfect. It is about 60 percent effective, according to recent data from the Centers for Disease Control and Prevention. But the CDC and other public health officials maintain that once-a-year flu shots are the best way to avoid the flu.

Masking, meanwhile, is a common method of preventing the spread of germs. Health care workers normally wear masks during surgeries and in other medical settings.

Dr. Robert A. Klugman, chief quality officer at UMass Memorial Medical Center, said the requirement to wear a mask is no different from other requirements of health care workers. UMass Memorial employees, for example, must be tested annually for tuberculosis. Pediatric workers must be vaccinated for measles and German measles.

In years past, influenza has killed tens of thousands of people in the United States. Hundreds of people are admitted to UMass Memorial every year because of the flu, and some of them die.

“God forbid we found someone here wasn't protecting themselves, passing the flu on, and someone died,” Dr. Klugman said. “That would be a tragedy. So I think most people have to search their souls around this issue.”

Lynne P. Starbard, co-chairwoman of the bargaining unit for the Memorial and Hahnemann campuses, and a maternity nurse at Memorial, said the masking policy is a workers' rights issue.

“There are people who have had bad reactions to the vaccine,” she said. “They're being penalized.”

The disagreement over masking comes as nurses and administrators continue tense contract negotiations.

Some states require mandatory flu vaccination for health care workers. Massachusetts does not, but the state requires hospitals to make flu shots available to their workers.

The Massachusetts Hospital Association supports mandatory vaccination. The state Department of Public Health wants hospitals to vaccinate at least 90 percent of their workers. Vaccination rates rose at many hospitals last flu season, compared to the season before, according to department figures. But just 18 hospitals out of 74 statewide reached the 90 percent threshold.

St. Vincent Hospital in Worcester, which vaccinated 80 percent of its workers last flu season, is implementing a masking policy this winter, but milder than the policy at its neighbor UMass Memorial. Employees who refuse the flu shot will be asked to wear masks when they're within 6 feet of a patient — but only during an influenza surge, a hospital spokeswoman said.

Dr. William G. Buchta, director of occupational health at the Mayo Clinic in Minnesota, said health officials place too much emphasis on the flu vaccine.

“The research has shown you don't need 100 percent of your health care workers to be vaccinated to protect your patients,” he said.

Telling people the vaccine is an excellent form of flu prevention, he added, gives a false sense of security.

The CDC recommends flu vaccines for almost everyone older than 6 months. Some people should not take the vaccine for medical reasons — for example, if they're allergic to eggs.

Some people choose not to take the vaccine for religious reasons. Some simply don't believe in it.

Ms. Smith, the nurse at University Campus, said good hygiene and frequent hand-washing is more important than vaccines.